Three Point Functions in the N=4 Orthogonal Coset Theory

TL;DR

This paper constructs higher spin currents in an orthogonal coset theory and computes their three-point functions with scalars, revealing their behavior in finite and large N limits, extending the understanding of superconformal algebras.

Contribution

It introduces explicit constructions of higher spin currents in the SO(N+4)/[SO(N) x SO(4)] coset and calculates their three-point functions, connecting nonlinear and linear superconformal algebra extensions.

Findings

Explicit higher spin-2 current constructed

Three-point functions computed for finite N and k

Large N limit shows coincidence of nonlinear and linear results

Abstract

We construct the lowest higher spin-2 current in terms of the spin-1 and the spin-1/2 currents living in the orthogonal SO(N+4)/[SO(N) x SO(4)] Wolf space coset theory for general N. The remaining fifteen higher spin currents are determined. We obtain the three-point functions of bosonic (higher) spin currents with two scalars for finite N and k (the level of the spin-1 current). By multiplying SU(2) x U(1) into the above Wolf space coset theory, the other fifteen higher spin currents together with the above lowest higher spin-2 current are realized in the extension of the large N=4 linear superconformal algebra. Similarly, the three-point functions of bosonic (higher) spin currents with two scalars for finite N and k are obtained. Under the large N 't Hooft limit, the two types of three-point functions in the nonlinear and linear versions coincide as in the unitary coset theory found previously.